Trilemma

A trilemma is a difficult choice from three options, each of which is (or appears) unacceptable or unfavourable.

There are two logically equivalent ways in which to express a trilemma: it can be expressed as a choice among three unfavourable options, one of which must be chosen, or as a choice among three favourable options, only two of which are possible at the same time.

The term derives from the much older term dilemma, a choice between two or more difficult or unfavourable alternatives.

The earliest recorded use of the term was by the British preacher Philip Henry in 1672, and later, apparently independently, by the preacher Isaac Watts in 1725.[1]

One well known trilemma is sometimes used by Christian apologists as a proof of the divinity of Jesus,[4] and is most commonly known in the version by C. S. Lewis. It proceeds from the assumption that Jesus claimed to be God, and that therefore one of the following must be true:[5]

Lunatic: Jesus was not God, but he mistakenly believed that he was.

Liar: Jesus was not God, and he knew it, but he said so anyway.

Lord: Jesus is God.

The trilemma, usually in Lewis' formulation, is often used in works of popular apologetics, although it is almost totally absent from discussions about the status of Jesus by professional theologians and biblical scholars.[6] In his 1993 book The Metaphor of God Incarnate, John Hick recalled having been taught this argument as a child, and states that New Testament scholars today do not support the view that Jesus claimed to be God.[7]

The "cruel trilemma"[8] was an English ecclesiastical and judicial weapon[9] developed in the first half of the 17th century, and used as a form of coercion and persecution. The format was a religious oath to tell the truth, imposed upon the accused prior to questioning. The accused would find themselves trapped between:

A breach of religious oath if they lied (taken extremely seriously in that era, a mortal sin,[8] and perjury);

In the theory of knowledge the Münchhausen trilemma is a philosophical term coined to stress the impossibility to prove any certain truth even in the fields of logic and mathematics. Its name is going back to a logical proof of the German philosopher Hans Albert. This proof runs as follows: All of the only three possible attempts to get a certain justification must fail:

All justifications in pursuit of certain knowledge have also to justify the means of their justification and doing so they have to justify anew the means of their justification. Therefore there can be no end. We are faced with the hopeless situation of an infinite regression.

One can stop at self-evidence or common sense or fundamental principles or speaking 'ex cathedra' or at any other evidence, but in doing so the intention to install certain justification is abandoned.

In Mill's On Liberty, as a part of his argument against the suppression of free speech, he describes the trilemma facing those attempting to justify such suppression (although he does not refer to it as a trilemma Leo Parker-Rees (2009) identified it as such). If free speech is suppressed, the opinion suppressed is either:[10]

True – in which case society is robbed of the chance to exchange error for truth;

False – in which case the opinion would create a 'livelier impression' of the truth, allowing people to justify the correct view;

Half-true – in which case it would contain a forgotten element of the truth, that is important to rediscover, with the eventual aim of a synthesis of the conflicting opinions that is the whole truth.

In 1952, the British magazine, The Economist, published a series of articles on an "Uneasy Triangle," which described "the three-cornered incompatibility between a stable price level, full employment, and . . . free collective bargaining." The context was the difficulty maintaining external balance without sacrificing two sacrosanct political values, jobs for all and unrestricted labor rights. Inflation resulting from labor militancy in the context of full employment put powerful downward pressure on the pound sterling. Runs on the pound triggered a long series of economically and politically disruptive "stop-go" policies (deflation followed by reflation).[11] John Maynard Keynes had anticipated the severe problem associated with reconciling full employment with stable prices without sacrificing democracy and the associational rights of labor.[12] The same incompatibilities were also elaborated on in Charles Lindblom's 1949 book, Unions and Capitalism.[13]

In 1962 and 1963, a trilemma (or "impossible trinity") was introduced by economists Robert Mundell and Marcus Fleming in articles discussing the problems with creating a stable international financial system. It refers to the trade-offs among the following three goals: a fixed exchange rate, national independence in monetary policy, and capital mobility. According to the Mundell–Fleming model of 1962 and 1963, a small, open economy cannot achieve all three of these policy goals at the same time: in pursuing any two of these goals, a nation must forgo the third.[14]

In 1989 Peter Swenson posited the existence of "wage policy trilemmas" encountered by trade unions trying to achieve three egalitarian goals simultaneously. One involved attempts to compress wages within a bargaining sector while compressing wages between sectors and maximizing access to employment in the sector. A variant of this "horizontal" trilemma was the "vertical" wage policy trilemma associated with trying simultaneously to compress wages, increase the wage share of value added at the expense of profits, and maximize employment. These trilemmas helped explain instability in unions' wage policies and their political strategies seemingly designed to resolve the incompatibilities.[15]

Steven Pinker noted another social trilemma in his books How the Mind Works and The Blank Slate: that a society cannot be simultaneously fair, free and equal. If it is fair, individuals who work harder will accumulate more wealth; if it is free, parents will leave the bulk of their inheritance to their children; but then it will not be equal, as people will begin life with different fortunes.

Arthur C. Clarke cited a management trilemma encountered when trying to achieve production quickly and cheaply while maintaining high quality.[16] In the software industry, this means that one can pick any two of: fastest time to market, highest software quality (fewest defects), and lowest cost (headcount). This is the basis of the popular project management aphorism "Quick, Cheap, Good: Pick two," conceptualized as the project management triangle.

The RAID technology may offer two of the three desirable value: (relative) inexpensiveness, speed or reliability (RAID0 is fast and cheap, but unreliable; RAID60 is extremely expensive and reliable, with correct performance and so on). The phrase "fast, cheap, good: choose two".

It had been pastiched in silent computing as "fast, cheap, quiet: choose two".

Further trilemma in computing include the CAP theorem about guarantees provided by distributed systems, and Zooko's triangle for naming participants in network protocols.

The “Žižek trilemma” is a humorous formulation on the incompatibility of certain personal virtues under a constraining ideological framework. Often attributed to the philosopher Slavoj Žižek, it is actually quoted by him as the product of an anonymous source:

One cannot but recall here a witty formula of life under a hard Communist regime: Of the three features — personal honesty, sincere support of the regime and intelligence — it was possible to combine only two, never all three. If one were honest and supportive, one was not very bright; if one were bright and supportive, one was not honest; if one were honest and bright, one was not supportive.[19]

^Davis, Stephen T.; Kendall, Daniel; O'Collins, Gerald (2004). "Was Jesus Mad, Bad, or God?". The Incarnation: an interdisciplinary symposium on the Incarnation of the Son of God. Oxford University Press. pp. 222–3.

^Hick, John. The Metaphor of God Incarnate. p. 27. A further point of broad agreement among New Testament scholars ... is that the historical Jesus did not make the claim to deity that later Christian thought was to make for him: he did not understand himself to be God, or God the Son, incarnate. ... such evidence as there is has led the historians of the period to conclude, with an impressive degree of unanimity, that Jesus did not claim to be God incarnate.

^Mill, John Stuart (1869) [1859]. "Chapter II: Of the Liberty of Thought and Discussion". On liberty (4th ed.). London: Longman, Roberts & Green. ISBN1-58734-034-8. Retrieved 10 September 2014. (§1).. If the opinion is right, they are deprived of the opportunity of exchanging error for truth: if wrong, they lose, what is almost as great a benefit, the clearer perception and livelier impression of truth, produced by its collision with error. .. (§34) .. But there is a commoner case than either of these; when the conflicting doctrines, instead of being one true and the other false, share the truth between them; and the nonconforming opinion is needed to supply the remainder of the truth, of which the received doctrine embodies only a part.

^Editorial, "The Uneasy Triangle," The Economist, August 9, 16, and 23, 1952.